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Office:
Stratton Hall, 202C
Phone: +1-508-831-5242
Fax: +1-508-831-5824
silviajimenez@wpi.edu

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Silvia Jiménez

My research interests are in nonlinear partial differential equations and homogenization theory with applications to material sciences. In composite materials, failure initiation is a multi-scale phenomenon. A load applied at the structural scale is often amplified by the microstructure creating local zones of high field concentration. Therefore, it is relevant to assess the load transfer between macroscopic and microscopic length scales. In my thesis, I investigated the properties of the local fields inside mixtures of two nonlinear power-law materials, and developed new multi-scale tools to bound the local singularity strength inside micro-structured media in terms of the macroscopically applied fields. This simple constitutive model is frequently used to describe several phenomena, ranging from plasticity to optical nonlinearities in dielectric media.

Currently, I have been investigating neutral inclusions. If a neutral inclusion is inserted in a matrix containing a uniform applied electric field, it does not disturb the field outside the inclusion. The well-known Hashin coated sphere is an example of a neutral coated inclusion. In my research, I consider the problem of constructing neutral inclusions from nonlinear materials.

Teaching has always been one of the greatest and most satisfying experiences in my life. Before going to graduate school, I worked as an instructor for the Department of Mathematics at Universidad de Costa Rica. As a Teaching Assistant at Louisiana State University, I received two certificates of Teaching Excellence and I was awarded the David Oxley Memorial Graduate Student Teaching Award. My experience teaching at WPI has been the most enjoyable. WPI students are hardworking and eager to learn. It is a rewarding experience after seven intense weeks of class to know that you and your students have accomplished a goal.

Research Interests

• Mathematical Material Sciences
• Partial Differential Equations
• Homogenization Theory for Nonlinear Partial Differential Equations
• Multi-scale Analysis

Education

• BS, Universidad de Costa Rica, 2002
• MS, Louisiana State University, 2006
• PhD, Louisiana State University, 2010

Featured Publications

• S. Jimenez, R.P. Lipton. "Correctors and Field Fluctuations for the $p_{\epsilon}(x)$-Laplacian with Rough Exponents". J.Math. Anal. Appl., 2010.
• S. Jimenez. "Correctors and Field Fluctuation for the $p_{\epsilon}(x)$-Laplacian with Rough Exponents with Sublinear Growth\$". Submitted for publication.
• S. Jimenez, B. Vernescu. "Nonlinear Neutral Inclusions: Assemblages of disks". arXiv:1201.4902v1.

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